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\section*{PCA -- excercise 07 \\\\ Heat-Relaxation/N-Body with OpenMP \\\\ \tiny{group: pra05 -- Matthias Heisler, Steffen Lammel}}

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\subsection*{Heat Relaxation}
The runtime of the sequential version with 1000 elements was $12.100976$ seconds. If we compare this result to the fastest OpenMP implementation, we get a Speed-Up of:\\

\begin{center}
$S = \frac{12.100976s}{3.71503s} = 3.26$
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\noindent
Interestingly, the parallel implementation can hardly achieve any speed-up on big working sets on the Xeon CPU of the creek machines, as we can see in the figure below.\\

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\space & \includegraphics[page=1,scale=.8]{01_heatrelax-openmp/result.pdf} & \space \\
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\noindent
On a similar machine, which houses an old AMD PhenomII 940, the speed-up is noticeable. All workloads perform best at 4 Threads, which is the number of physical CPUs of the machine.\\

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\space & \includegraphics[page=1,scale=.8]{01_heatrelax-openmp/result_pII940.pdf} & \space \\
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\subsection*{N-Body}
The runtime of the sequential version with 1000 bodys was $19.011$ seconds. If we compare this result to the fastest OpenMP implementation, we get a Speed-Up of:\\

\begin{center}
$S = \frac{19.011s}{3.273s} = 5.80$
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\noindent
Although the creek machines have only 4 physical CPUs, this speed-up can be explained by the caches. Every CPU has serveral MB of cache. Now, that we utilize all of them, the problem can be split-up and fit into the caches. SMT (Hyperthreading) should also be kept in mind. As we can see in the figure below, the best performance is achieved at 8 threads. This suggests that SMT is beneficial in this kind of application.\\
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\space & \includegraphics[page=1,scale=.9]{02_nbody/result.pdf} & \space \\
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